# Clearly mark answers to the multiple choice problems on your... 1. [5 pts] Find the limit, if it...

```Clearly mark answers to the multiple choice problems on your paper and your scantron.
1. [5 pts] Find the limit, if it exists for
lim
x 2
3

x  2
 1.
(a) - 1
(b) 1
(c)

(d)  
(e) none of these
______________________________________________________________________________________
2. [5 pts] Find the limit, if it exists for
(a) 1
(b)
4
7
(c) d.n.e.
(d) 0
(e) none of these
lim
x  1
x
x
2
 2x  3
2
 5x  6
.
3. [5 pts] How long will it take a population of 25 bacteria to triple at a growth rate of 5%?
(a) t 
ln 3
. 05
(b) t 
ln 3
5
(c)
t 
 3 
ln 

 25 
. 05
(d)
t 
 3 
ln 

 25 
5
(e) none of these
______________________________________________________________________________________
4. [5 pts] Find all points at which
(a) (   ,  1 )  (  1, 0 )
(b) (  1, 0 )  ( 0 , 1 )
(c) ( 0 , 1)  ( 1,  )
(d) (   ,  1)  ( 1,  )
(e) none of these
ln (1  x )
ln (1  x )
is continuous.
5. [5 pts] Find a value c so that the following function is continuous for all values of x:

1  x , x  2
f (x)  

 cx  1 , x  2
2
(a) 0
(b) 1
(c) - 1
(d) 2
(e) none of these
_____________________________________________________________________________________
6. [5 pts] Which of the following functions corresponds with the semilog graph below.
(a) y 
1
x  1
(b) y 
2
1
log x
2
(d)
y 
1
10

10

x
(e) none of these
(c)
y  10
x
2

1
10
7. [5 pts] Find the limit, if it exists for
lim
4 cos x  4  3 sin x
x 0
(a)
.
5x
3
5
(b)
4
5
(c) 
4
5
(d)
0
(e) none of these
_______________________________________________________________________________________
8. [5 pts] Find the limit, if it exists for
(a) - 1
(b) 1
(c)

(d)  
(e) none of these
lim
x  
x
2
1  x
.
9. [5 pts] Use a logarithmic transformation to find a linear relationship between appropriate transformations of
x and y if y  4 x 5 .
(a) log y  4 x  log 5
(b) log y  5 x  log 4
(c) log y  5 log x  log 4
(d) log y  4 log x  log 5
(e) none of these
_________________________________________________________________________________________
10. [5 pts] Let
f (x)  x
4
 x
3
 x  1.
Using the Intermediate Value Theorem and the Bisection Method,
what is the smallest interval on which we can conclude that f ( x ) has a root?
(a) (- 1, 0)
(b) (0, 1)

(c)  0 ,

1

2
1

, 0
2

(d) 
(e) none of these
11. [10 pts.] (a) Graph f ( x )  e x and show that it is one to one. Graph f ( x )  ln x and show
algebraically that it is the inverse of f ( x )  e x . List the domain and range of each function.
(b) Solve log ( x 2  1)  log ( x  1)  1
(a)
12. [10 pts.] Given
f (x) 
1

 1 , x 2

(
x

3
)


2 ,
x  2

,
definition of continuity if f ( x ) is continuous at x = 2.
carefully graph f ( x ) and determine by the 3 step
13. [5 pts. each] Compute each of the following limits.
(a)
lim
2x
2
x  0
(b)
lim
x  0
e


 

 10 
cos 

 x 
 1


x

1
x  1
14. Given the doublelog plot below, find a functional relationship between x and y.
15. [10 pts] (a) Use the limit definition of the derivative to find f  ( x ) for f ( x ) 
(b) Find the equation of the tangent to f ( x ) 
2x  1
at x = 1.
2x  1
.
MATH 147
EXAM I
NAME ___________________________________________
SECTION # _______________
SEAT # ____________